Mr. Kim also promised to visit Seoul, the South Korean capital, which would make him the first North Korean leader to make such a trip. That visit to the North Korean capital saw him again play the role of peacemaker as talks between the U.S. and North Korea appeared on the verge of collapsing.
Moon said he will carry a private message from Kim for Trump when he meets the USA president in NY next week at a United Nations meeting.
Kim pledged to work toward the "complete denuclearization of the Korean peninsula" during two meetings with Moon and his encounter with Trump, but follow-up negotiations on how to implement the vague commitments have since faltered.
Kim also wants a second summit with U.S. President Donald Trump as soon as possible.
"While this (the outcome of the third inter-Korean summit) may look small. our role is to hand over (the conversation) to the U.S.", Lee said.
"I have a dream that I have not been able to fulfil for a long time, which is trekking Mount Paektu and the Kaema Plateau [in North Korea]", Moon said during a banquet after his first summit with Kim in April, which took place at the demilitarised zone separating the two neighbours.
A copy of an article of the North's official newspaper Rodong Sinmun dated December 26, 1980 calls Mount Paektu a "sacred mountain of revolution" spearheaded by Kim Il Sung "in the flames of the arduous 20-year anti-Japan struggle".
But more eye-catching to Washington was his promise to dismantle a missile engine-test facility and a missile launchpad in northwest North Korea that have been essential to the country's development of intercontinental ballistic missiles, and invite outside experts to watch.
President Trump said Wednesday that "tremendous progress" was being made toward North Korea giving up nuclear weapons.
The two countries also agreed to engage "in constant communication and close consultations" to review the implementation of the previously signed Panmunjom Declaration "and prevent accidental military clashes by promptly activating the Inter-Korean Joint Military Committee". He didn't indicate in his brief remarks whether the US would be willing to take further steps to encourage North Korean action on denuclearization. On Thursday, Moon announced the two Koreas wish to make a declaration formally concluding the 1950-53 conflict by the end of 2018.
Earlier in the day, the leaders smiled broadly as they posed at the summit of Paektu, their wives grinning at their sides, a brilliant blue sky and the deep crater lake that tops the volcano in the background.
Mr Kim promised to accept global inspectors to monitor the closing of a key missile test site and launch pad and to visit Seoul soon, and both leaders vowed to work together to try to host the Summer Olympics in 2032.
After the two leaders pledged new steps aimed at salvaging nuclear talks on Wednesday, Moon and Kim made a decision to use the final day of their three-day summit to go up the symbolic mountain on the Chinese border together.
"A peace treaty would be sealed, as well as normalisation of North Korea-US relations, after the North achieves complete denuclearisation".
By the end of the day, both leaders had signed a joint agreement supporting the destruction of Kim's nuclear missile facilities, further actions towards officially ending the Korean War once and for all, as well as a plan to pursue a joint bid to host the 2032 Olympic Games. It features prominently in the North's propaganda, which extols the mountain as the birthplace of Kim Jong Il, the father of current leader Kim.